TSTP Solution File: GRP376-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP376-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:18:44 EDT 2023
% Result : Unsatisfiable 0.18s 0.71s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 37
% Syntax : Number of formulae : 160 ( 15 unt; 10 typ; 0 def)
% Number of atoms : 385 ( 384 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 322 ( 87 ~; 235 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
sk_c7: $i ).
tff(decl_26,type,
sk_c6: $i ).
tff(decl_27,type,
sk_c5: $i ).
tff(decl_28,type,
sk_c3: $i ).
tff(decl_29,type,
sk_c4: $i ).
tff(decl_30,type,
sk_c1: $i ).
tff(decl_31,type,
sk_c2: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c7) != sk_c6
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X2,sk_c5) != sk_c7
| inverse(X2) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_10 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
prove_this_23 ).
cnf(c_0_33,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_15 ).
cnf(c_0_35,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
prove_this_28 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
prove_this_9 ).
cnf(c_0_42,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_21 ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_22 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_42]),c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_11 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
prove_this_2 ).
cnf(c_0_50,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_26 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_25 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c5
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_6 ).
cnf(c_0_55,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
prove_this_14 ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_1 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c7) != sk_c6
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X2,sk_c5) != sk_c7
| inverse(X2) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c5) != sk_c6 ),
prove_this_31 ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_17 ).
cnf(c_0_63,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c5
| multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c7 ),
prove_this_27 ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_12 ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
prove_this_4 ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X1,sk_c5) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c5) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c5
| inverse(X4) != sk_c7 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_61]),c_0_28]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_74,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_63]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_30 ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_48]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_68]) ).
cnf(c_0_81,negated_conjecture,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_69]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_47,c_0_70]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| sk_c7 = identity
| multiply(X1,sk_c5) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c5) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c5
| inverse(X4) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_28]) ).
cnf(c_0_85,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c4) = sk_c6 ),
prove_this_29 ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c5
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c7) = sk_c1
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_47,c_0_79]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c7) = sk_c1
| inverse(sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_47,c_0_80]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c7) = sk_c6
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| sk_c7 = identity
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c5) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(sk_c4) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c5
| inverse(X3) != sk_c7 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c5) = sk_c2 ),
inference(spm,[status(thm)],[c_0_47,c_0_85]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c6
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_86]),c_0_28]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
prove_this_5 ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_34]) ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c7) = sk_c6
| sk_c3 != sk_c6 ),
inference(ef,[status(thm)],[c_0_89]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c7) = sk_c1
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_81,c_0_90]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| sk_c3 = sk_c6
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c5) = sk_c2
| sk_c7 = identity
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c5) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c5
| inverse(X3) != sk_c7 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| sk_c7 = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( sk_c6 = sk_c7
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_96]),c_0_28]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| sk_c1 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c5) = sk_c2
| sk_c7 = identity
| multiply(X1,sk_c5) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c5
| inverse(X2) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_47])]) ).
cnf(c_0_108,negated_conjecture,
( sk_c6 = identity
| sk_c7 != identity ),
inference(ef,[status(thm)],[c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( sk_c1 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c5) = sk_c2
| sk_c7 = identity
| multiply(X1,multiply(X2,sk_c5)) != sk_c7
| inverse(multiply(X1,X2)) != sk_c5
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7 ),
inference(spm,[status(thm)],[c_0_107,c_0_27]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_16 ).
cnf(c_0_112,negated_conjecture,
sk_c6 = identity,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_28])]),c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c4) = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_56,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c5) = sk_c2
| sk_c7 = identity
| inverse(multiply(X1,sk_c4)) != sk_c5
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7 ),
inference(spm,[status(thm)],[c_0_110,c_0_84]) ).
cnf(c_0_115,negated_conjecture,
sk_c5 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_29]),c_0_112]),c_0_42])]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c6) = sk_c4
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_113]) ).
cnf(c_0_117,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c7) = sk_c3
| inverse(sk_c1) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_91]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
prove_this_3 ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c7) = sk_c2
| sk_c7 = identity
| inverse(multiply(sk_c7,sk_c4)) != sk_c7
| multiply(X1,sk_c7) != identity
| inverse(X1) != sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_112]),c_0_42]),c_0_112])]),c_0_115]),c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( sk_c4 = identity
| sk_c7 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_112]),c_0_117]),c_0_112]),c_0_117]),c_0_112])]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c7) = sk_c3
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_118,c_0_109]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_119]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c7) = sk_c2
| sk_c7 = identity
| multiply(X1,sk_c7) != identity
| inverse(sk_c7) != sk_c7
| inverse(X1) != sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_42]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c7) = sk_c3
| sk_c7 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_112]),c_0_117]),c_0_112])]) ).
cnf(c_0_126,negated_conjecture,
( sk_c7 = identity
| sk_c3 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_112]),c_0_42]),c_0_112]),c_0_117]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_63,c_0_75]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| sk_c7 = identity
| sk_c2 = sk_c3
| multiply(X1,sk_c7) != identity
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).
cnf(c_0_129,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c5) = sk_c2 ),
inference(spm,[status(thm)],[c_0_47,c_0_65]) ).
cnf(c_0_130,negated_conjecture,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| sk_c2 = sk_c3
| sk_c7 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_28]),c_0_47])]) ).
cnf(c_0_132,negated_conjecture,
( inverse(sk_c5) = sk_c2
| inverse(sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_47,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| inverse(sk_c4) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_112]),c_0_42]),c_0_115]),c_0_115]),c_0_115]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c7,sk_c7) = identity
| sk_c7 = identity
| sk_c2 = sk_c7 ),
inference(spm,[status(thm)],[c_0_131,c_0_126]) ).
cnf(c_0_135,negated_conjecture,
( inverse(sk_c6) = sk_c7
| sk_c6 = sk_c7
| sk_c4 != sk_c7 ),
inference(ef,[status(thm)],[c_0_116]) ).
cnf(c_0_136,negated_conjecture,
( inverse(sk_c7) = sk_c3
| inverse(sk_c7) = sk_c2 ),
inference(rw,[status(thm)],[c_0_132,c_0_115]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| inverse(sk_c7) = sk_c4 ),
inference(spm,[status(thm)],[c_0_47,c_0_133]) ).
cnf(c_0_138,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c7
| sk_c7 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_134]),c_0_42]) ).
cnf(c_0_139,negated_conjecture,
( sk_c7 = identity
| sk_c4 != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_112]),c_0_117]),c_0_112])]) ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c7) = sk_c3
| sk_c2 != sk_c3 ),
inference(ef,[status(thm)],[c_0_136]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| sk_c7 = identity
| sk_c2 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| sk_c4 = sk_c3
| sk_c2 != sk_c3 ),
inference(spm,[status(thm)],[c_0_140,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( sk_c2 = sk_c7
| sk_c7 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_141]),c_0_28])]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| sk_c3 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_112]),c_0_42]),c_0_115]),c_0_115]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| sk_c7 = identity
| sk_c4 = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_146,negated_conjecture,
( sk_c4 = sk_c3
| sk_c7 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_145]),c_0_28])]) ).
cnf(c_0_147,negated_conjecture,
( multiply(X1,sk_c7) != identity
| multiply(X2,sk_c7) != sk_c7
| multiply(X3,sk_c7) != identity
| inverse(sk_c7) != identity
| inverse(sk_c7) != sk_c7
| inverse(X1) != identity
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_112]),c_0_29]),c_0_112]),c_0_42]),c_0_112]),c_0_112]),c_0_42]),c_0_112]),c_0_112]),c_0_112])])]),c_0_115]),c_0_115]),c_0_115]),c_0_115])]) ).
cnf(c_0_148,negated_conjecture,
sk_c7 = identity,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_146]),c_0_126]) ).
cnf(c_0_149,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148]),c_0_42]),c_0_148]),c_0_42]),c_0_148]),c_0_148]),c_0_42]),c_0_148]),c_0_117]),c_0_148]),c_0_117]),c_0_148]),c_0_148]),c_0_148])])])])]),c_0_117])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP376-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:45:04 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.54 start to proof: theBenchmark
% 0.18/0.71 % Version : CSE_E---1.5
% 0.18/0.71 % Problem : theBenchmark.p
% 0.18/0.71 % Proof found
% 0.18/0.71 % SZS status Theorem for theBenchmark.p
% 0.18/0.71 % SZS output start Proof
% See solution above
% 0.64/0.72 % Total time : 0.152000 s
% 0.64/0.72 % SZS output end Proof
% 0.64/0.72 % Total time : 0.155000 s
%------------------------------------------------------------------------------